AM-Align: Globally Optimal Estimation of Accelerometer–Magnetometer Misalignment

Misalignment estimation of the accelerometer-magnetometer (AM) combination is crucial for accurate attitude and position estimation in various applications. Despite significant research efforts over the past decades, existing algorithms rely on sufficient and outlier-free data to guarantee a satisfactory initial guess for optimization. This article presents AM-Align, a novel globally optimal method that addresses this limitation. The key innovation of AM-Align is its ability to find all global optima by identifying the solution set with the least loss function values using the polynomial eigenvalue method, making it independent of initial guesses and robust to insufficient data and outliers. Simulation studies demonstrate the complete solution set for the minimal case of the AM calibration problem, providing valuable insights. Experimental results showcase the superiority of AM-Align compared to state-of-the-art methods, requiring fewer measurements while achieving higher accuracy and robustness. Notably, AM-Align outperforms representative algorithms by a significant margin in terms of calibration precision and resilience to data scarcity and outliers. This work presents a significant advancement in AM calibration, enabling more reliable attitude and position estimation in real-world scenarios. We will make the AM-Align codebase (https://github.com/JokerJohn/AM_Align) publicly available to the community, further advancing the development of this field.